Ivan, if you liked Burnout... then why not Burnout? I'll assume you played 2 or 3 on consoles. Burnout Paradise is a fun open-city racing game with tons of secrets. I think it gets stale quickly but maybe I'm past my racing craze. It's going to get remastered in the coming months but with zero info I'll asume your PC will accomodate a 2010 game better.
Speaking of games for weak computers, Megarace 2 is now on Steam and it's so cheap it would be a shame to miss it. In short it's a sci-fi racing game with mines and missiles. Good steering feeling, nice visuals especially for a DOS game from more than 20 fucking years ago, the jungle in particular looks amazing. Skip Megarace 1 as it's too primitive for comfort, and skip Megarace 3 as it's too shit for comfort.
Other games with power-ups are Rollcage and its recent clone named GRIP. Rollcage I Redux and Rollcage II Extreme are both free upgrades / remakes and will give you a great time.
Split/Second is a bit like MotorStorm in that it's a modern-setting racing game with power-ups that can alter the environment and change the layout of the tracks, for example by collapsing buildings. It has a lot of potential but you should definitely try before you buy because it forces you to drive like a complete moron in order to grind your power-ups.
Speaking of MotorStorm, assuming your computer can handle it, you can always emulate it and give it a look. I wouldn't put it very high on your list because the driving doesn't feel fast and nervous at all. It's broken on PPSSPP (no sound) so you are stuck with PCSX2.
Speaking of what you can get on PPSSPP, make sure to check both Legends and Dominator. Dominator is typical of a slightly improved sequel except they ditched the crash mode entirely (no big loss). Both will give you a great time as the driving is both slick and precise, but also extremely fast and intense.
Relevant links:
Burnout Paradise on Steam
Megarace 2 on Steam
Split/Second on Steam
GRIP on Steam
Rollcage I Redux on... whoever that is' blog
Rollcage II Extreme, same source
Not linked:
Burnout Legends (PSP)
Burnout Dominator (PSP)
Motorstorm Artic Edge (PS2)
Just so the admins don't get into trouble. I'm sure you know how to get them through the usual channels.